According to the National Health Survey, the heights of adult males in the Unite

Question

According to the National Health Survey, the heights of adult males in the United States are normally distributed with mean 69.0 inches and standard deviation 2.8 inches.

(a) What is the probability that an adult male chosen at random is between 64 and 74 inches tall? (Round your answer to three decimal places.)


(b) What percentage of the adult male population is more than 6 feet tall? (Round your answer to one decimal place.)
%

Section 8.5 e Dwww.webassign.net/web/Student/Assignment-Responses/last?dep-13189104 For this assignment, you submit answers by questions ssignment S coring Y our best submission for each question part is used for your score in points scalcET8 8.5014, 0/3 Submissions Used According to the National Health Survey, the heights of adult males in the United States are normally distributed with mean 69.0 inches and standard deviation 2.8 inches (a) What is the probability that an adult male chosen at random is betwen 64 and 74 inches tall (Round your answer to three dedimal places.) (b) What percentage of the adult male population is more than 6 feet tall? (Round your answer to one decimal place.) Submit Ans wer Save Progress Submit Answer Save Progress

Explanation / Answer

Normal Distribution
Mean ( u ) =69
Standard Deviation ( sd )=2.8
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 64) = (64-69)/2.8
= -5/2.8 = -1.7857
= P ( Z <-1.7857) From Standard Normal Table
= 0.03707
P(X < 74) = (74-69)/2.8
= 5/2.8 = 1.7857
= P ( Z <1.7857) From Standard Normal Table
= 0.96293
P(64 < X < 74) = 0.96293-0.03707 = 0.9259                  

b.
P(X > 72) = (72-69)/2.8/ Sqrt ( 1 )
= 3/2.8= 1.0714
= P ( Z >1.0714) From Standard Normal Table
= 0.142  

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